Description
Two’s-Complement
The two’s-complement representation of a non-negative integer is simply its standard representation in base 2. However, the two’s-complement representation of a negative integer is obtained by first finding the base-2 representation of its absolute value, then flipping each bit, and finally adding the number 1.
This problem has two parts.
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First, write a function called TcToNum that takes as input a string of 8 bits representing an integer in two’s-complement, and returns the corresponding integer. Notice here that since the input string is always exactly 8 bits long, we will often have leading 0s in the input, as in “00000001”. Here is sample input and output:
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TcToNum(“00000001”)
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1
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TcToNum(“11111111”)
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-1
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TcToNum(“10000000”) -128
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TcToNum(“01000000”)
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64
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Next, write a function called NumToTc that takes as input an integer N, and returns a string representing the two’s-complement representation of that integer. You should assume that exactly 8 bits are being used, so only a certain range of numbers can be represented! The output should be exactly 8 bits long in all cases. If the input N is such that it cannot be represented in two’s-complement with 8 bits, the function should return “Error”. Here is some sample input and output:
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NumToTc(1)
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‘00000001’
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NumToTc(-128) ‘10000000’
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NumToTc(200)
‘Error’
